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Pythagorean Inequality

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The Pythagorean Inequality is a generalization of the Pythagorean Theorem. The Theorem states that in a right triangle with sides of length a \leq b \leq c we have a^2 + b^2 = c^2. The Inequality extends this to obtuse and acute triangles. The inequality says:

For an acute triangle with sides of length a \leq b \leq c, a^2+b^2>c^2. For an obtuse triangle with sides a \leq b \leq c, a^2+b^2<c^2.

This inequality is a direct result of the Law of Cosines, although it is also possible to prove without using trigonometry.

See also

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